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Math Help - Infinite/Maclaurin Series problem!!

  1. #1
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    Infinite/Maclaurin Series problem!!

    Evaluate the following: Riemann Sum k=2 to infinity, 2/(k^2 -1)

    I'm not really sure where to begin...I rearranged the equation to -2/( 1 - k^2) and used the Maclaurin Series for 1/(1 - x) to obtain -2 * k^(2n). Interval of convergence for k is -1 < k < 1. Now I'm stuck as to how to evaluate it.
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  2. #2
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    Re: Infinite/Maclaurin Series problem!!

    Remember partial fractions:

    {2\over k^2-1}={1\over k-1}-{1\over k+1}

    Now see if you have a telescoping series. By the way this is a series not a Riemann sum.
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  3. #3
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    Re: Infinite/Maclaurin Series problem!!

    Achiu 17
    for k=2 till infinity Σ[2/(k^2 -1]=3/2 easy.
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